1. Presentation

2. The Further Mathematics Support Programme
Our aim is to increase the uptake of AS and A level Further Mathematics to ensure that more students reach their potential in mathematics.
The FMSP works closely with school/college maths departments to provide professional development opportunities for teachers and maths promotion events for students.
To find out more please visit

3. Game,
Set,
Maths
Cath Moore
E&E Conference 2016

4. Using sports Gives you a hook to get students interested
does the sport matter?
Use the situation as a reason to develop the maths
Is based in real life
Is messy
Needs estimation and approximation
Needs modelling

5. Tennis – why? Most students familiar with the basics
Most students have the opportunity to play
Scoring system is not a straightforward as football
Tournaments tend to be over a concentrated time period
Lots of maths involved 
Get a cool title for the session…
How about rugby?

6. How can you win a game? Tennis scores: 0, 15, 30, 40, win
Players need to win by two points, so if get to (deuce) winner gets A then win.
How can a player win? What are the possible scoring lines?
Develops: listing, systematic listing, logical thinking
Extend to: if all outcomes are equally likely, what is the average number of points per game

7. Average points score per game
Presentation
Average points score per game
Possible outcomes: 0-w, 15-w, 30-w, 40-w;
Points per game: 4, 5, 6, 7….
9...or 11…or 19…
We need some real data…

8. Average points Men’s singles: 28 805 points in 127 matches = 226.8 ppm
Women’s singles:
points in 127 matches = ppm
So it seems reasonable that men are paid more than women as they play more points…
unless you calculate it by game…
Men’s singles: ÷4759 = 6.05 ppg
Women’s singles: ÷ 2787 = 6.45 ppg
Which must make women’s games more exciting to watch…

9. Ways to win a set
To win a set you have to score two more games than your opposition, unless you get to 6-6 when you have a tiebreak unless it is the final set. The winner is the first to three sets for men.
How may different ways of winning a set are there?
Develops: problem solving skills, reasoning, systematic listing
Extend to: ways of winning matches

10. Average points score per set
How do we know how the set was won…
6-0, 6-1, 6-2, 6-3, 6-4, 7-5, 7-6 (which brings in tie breaks)…
or some other score up to (Isner bt Mahut 2010)
We could use real data…
GSM data.xlsx

11. What else could we investigate?

12. Probability of winning
Assuming that each player (Alan or Bob) is equally likely to win a game, what is the probability of a five set match?
Probability of winning in exactly 5 sets is 12/32
How did you do this?
How would you expect your students to do this?
Historically the probability of a 5 set match (looking at data since 1968) is about 32%...

13. Scheduling matches
Average length of match is approx 150min M (90min F)
Playing time per day is 1130 to approx 2100 (1300 start on Centre and No1 court)
How many matches can you fit on a court in one day?
19 grass courts – how many matches in a day altogether? (need to fit in 662 over the fortnight)
Develops logical thinking, reasoning processes – leads to maths covered in A level decision units

14. Reaction times
Can we calculate/estimate the reaction time for a successful return of serve?
Time = distance ÷ speed
Distance: 60’ to 78’
Speed (as recorded on speed camera) eg 127mph
Reaction time…
= 60'(to 78')/127mph
= 18m (to 23.4m)/55mps
= 0.3 to 0.4 seconds

15. Paying winners…
It was considered wrong that men were paid more than women and since 2007, the men’s singles and women’s singles winners have been paid the same amount… but is this fair?
Let’s take 2015 as an example…
Both winners won 7 matches including the final to win £1.88m, but…
Djokovic played a max 35 games (actually 24 games)
Williams played a max 21 games (actually 16 games)
So Djokovic averaged £54,000 (£78,000) per game
And Williams averaged £90,000 (£118,000) per game
Is this fair? Should we plan to pay women £36,000 extra per game?

16. Paying winners…
However, some people say that as each game lasts longer in women’s singles it is fairer to think about the time spent playing…
Djokovic played for 16 hours exactly
Williams played for 10 hours and 32 minutes
Djokovic was paid £118,000 per hour
Williams was paid £179,000 per hour
Could we have an hourly rate for winners depending on length of match?
The longest match was in 2010 when in the first round Isner beat Mahout after playing 183 games and taking 11hours and 5 minutes

17. Closing the angle
Closing the angle on the serve - where is best to stand - using geogebra?
returner off base line.ggb

18. Rugby questions Scoring – which score lines are possible?
What’s the force acting on the centre in the pack?
Where’s the best place to stand to take the conversion?
rugby angles.ggb
Do you have to do the ‘bottom out’ pose to kick well?

19. MEI Conference
Three-day event for mathematics teachers of all GCSE, Core Maths and A level specifications
25-27 June 2015 at the University of Bath
4 workshop sessions every day, each with 8 choices
3 informative and entertaining plenaries
En-suite accommodation available
Register online at conference.mei.org.uk

20. The Further Mathematics Support Programme
Our aim is to increase the uptake of AS and A level Further Mathematics to ensure that more students reach their potential in mathematics.
The FMSP works closely with school/college maths departments to provide professional development opportunities for teachers and maths promotion events for students.
To find out more please visit